This project addresses a variety of problems related to protein structure and folding, and uses methods developed in modern statistical mechanics. Of current interest is the problem of developing an objective measure of accuracy for protein strructures determined by multi-dimensional NMR measurements. Successful completion of this project would yield a measure of accuracy analogous to the R factor which is commonly used for assessing the accuracy of crystallographic structure determinations. A second closely related part of this project involves the development and exploration of a new technique for incorporating distance constraints into the statistical mechanical theory of protein structure. This new theoretical approach is based on replacing rigid constraints by more realistic "elastic" ones. The resulting framework for conformational analysis is also more tractable than previous methods in that it allows many calculations to be carried out simply and exactly. It is also planned to use this basic idea to extend earlier work on accuracy requirements for potential functions to yield accurate structure determinations. A further initiative uses neural network techniques to extract information on the secondary structure of proteins from chemical shift measurements made by NMR. So far a fast backpropagation program has been written for this project and tested on a related problem.